import collections


# 最初版本，超时
# class Solution:
#
#     def isNStraightHand(self, hand, W):
#         """
#         :type hand: List[int]
#         :type W: int
#         :rtype: bool
#         """
#         if W>len(hand):
#             return False
#         hand.sort()
#         if len(hand)%W!=0:
#             return False
#         dict_hand = collections.Counter(hand)
#         list_hand = [key for key,value in sorted(dict_hand.items(),key = lambda x:x[0])]
#         if W > len(list_hand):
#             return False
#         i = 0
#         while i < len(list_hand):
#             if dict_hand[list_hand[i]] != 0:
#                 # 循环查询
#                 for j in range(W):
#                     if list_hand[i]+j in list_hand:
#                         dict_hand[list_hand[i]+j]-=1
#                     else:
#                         return False
#             else:
#                 i +=1
#         return True

# 他人版本
# class Solution(object):
#     def isNStraightHand(self, hand, W):
#         """
#         :type hand: List[int]
#         :type W: int
#         :rtype: bool
#         """
#         n = len(hand)
#         if n%W != 0:
#             return False
#         hand.sort()
#         cts = collections.defaultdict(int)
#         for v in hand:
#             cts[v] += 1
#         for v in hand:
#             if cts[v] == 0:
#                 continue
#             for j in range(W):
#                 if cts[v+j] == 0:
#                     return False
#                 cts[v+j] -= 1
#         return True

# 改进后的版本，通过
class Solution:
    def isNStraightHand(self, hand, W):
        """
        :type hand: List[int]
        :type W: int
        :rtype: bool
        """
        if W > len(hand):
            return False
        hand.sort()
        if len(hand) % W != 0:
            return False
        dict_hand = collections.Counter(hand)
        set(hand)
        print(hand)
        if W > len(hand):
            return False
        i = 0
        for value in hand:
            if dict_hand[value] != 0:
                # 循环查询
                for j in range(W):
                    if dict_hand[value + j] != 0:
                        dict_hand[value + j] -= 1
                    else:
                        return False
            else:
                continue
        return True


def main():
    sol = Solution()
    print(sol.isNStraightHand(
        hand=[4101, 4647, 4719, 5882, 6666, 6829, 4574, 3356, 4867, 5365, 5222, 4322, 3686, 6648, 3866, 3782, 3037,
              7209, 6646, 4295, 6780, 3295, 7201, 3065, 4532, 5210, 4422, 7174, 3797, 5588, 3117, 4814, 7026, 6018,
              3878, 3245, 6363, 7222, 8294, 3596, 5254, 5352, 4107, 4110, 4302, 3896, 4002, 5937, 4348, 3701, 4201,
              4067, 4973, 4424, 8225, 5884, 5783, 6142, 6001, 5674, 6751, 3948, 6854, 7667, 7358, 7248, 6679, 3338,
              6882, 3089, 6558, 2916, 2694, 2688, 6962, 4236, 4005, 5108, 4556, 4278, 7416, 3036, 5216, 3604, 5695,
              4215, 6962, 8377, 6737, 4241, 8112, 3640, 3679, 7169, 8199, 6152, 7037, 6746, 6336, 6531, 5103, 4718,
              3913, 5636, 6893, 4431, 5523, 6880, 5856, 8342, 5302, 4140, 6301, 5536, 4546, 3296, 3205, 6044, 7385,
              2985, 6790, 6762, 5316, 4836, 5165, 3909, 4227, 5633, 4158, 5653, 2619, 3574, 6578, 6952, 4312, 3526,
              3640, 7427, 6104, 5862, 3821, 5564, 4217, 6718, 4294, 3357, 5377, 7170, 5230, 3370, 8302, 3535, 5423,
              5158, 4447, 8368, 7305, 4877, 5088, 7222, 7965, 7061, 6855, 3493, 3197, 3987, 4684, 5129, 5547, 2737,
              2623, 7160, 5348, 5610, 7597, 3394, 5123, 7042, 5461, 2680, 3963, 7210, 3206, 7266, 3396, 6221, 6706,
              5972, 4822, 6695, 8312, 7701, 4079, 6347, 4877, 3804, 2617, 2665, 4509, 6370, 6178, 6706, 3580, 4419,
              5595, 2649, 4685, 6057, 6224, 4136, 5627, 7033, 5970, 4758, 4978, 2663, 3109, 2538, 2728, 3554, 2817,
              4991, 7448, 5176, 5218, 3218, 3141, 7041, 3965, 4225, 4795, 5812, 2895, 6889, 5249, 3917, 8307, 5881,
              7411, 5940, 5587, 5886, 6296, 6543, 7471, 7280, 7420, 5925, 4924, 7413, 4701, 7337, 6941, 4183, 6992,
              7020, 3589, 5573, 4008, 6528, 4647, 8074, 6836, 3391, 3625, 6948, 7696, 6177, 2882, 8090, 7979, 5439,
              2959, 3463, 6489, 6459, 5396, 4837, 4962, 5584, 4416, 3624, 4906, 5801, 3420, 7061, 4045, 4744, 4324,
              7225, 4071, 3693, 6262, 2755, 7192, 5399, 6316, 6531, 7209, 5368, 4828, 6233, 3501, 7042, 4233, 2955,
              5449, 2730, 6745, 7354, 8279, 4409, 8380, 3790, 2491, 4533, 7766, 6944, 8107, 7338, 5797, 7704, 3653,
              4608, 4160, 2710, 6447, 4066, 3521, 4117, 7201, 3243, 6085, 6340, 6006, 7043, 6334, 6366, 7012, 6735,
              5734, 8055, 5056, 6504, 3086, 3776, 5312, 2656, 4482, 6441, 7251, 5815, 3639, 2707, 4286, 6488, 7252,
              3147, 3334, 5983, 7323, 4925, 6126, 5439, 5829, 6201, 3851, 4986, 8339, 6904, 5209, 5227, 7496, 4708,
              5639, 3878, 7795, 7053, 3306, 5229, 3755, 6254, 4518, 7400, 3244, 7531, 6291, 8311, 3557, 4916, 6182,
              5663, 6913, 4418, 6982, 3355, 6113, 7247, 3652, 5307, 4292, 7037, 4068, 5848, 7271, 4985, 3860, 4247,
              5825, 5300, 4411, 7240, 3733, 4466, 6093, 3832, 6655, 4413, 7286, 7933, 4576, 3876, 3815, 7054, 4152,
              7702, 6649, 5332, 3332, 4164, 6338, 7340, 6909, 3340, 5852, 6553, 6405, 6245, 7372, 7208, 8384, 4002,
              2898, 4418, 3182, 4491, 4298, 4676, 5501, 6218, 4473, 7006, 4850, 5274, 6724, 3234, 2722, 4336, 7141,
              4146, 2693, 3885, 4176, 6588, 2747, 6812, 5770, 4019, 3757, 4596, 2674, 7450, 6040, 5641, 2790, 6607,
              6451, 3421, 6263, 5221, 6845, 4208, 3660, 6228, 5807, 6124, 3004, 3217, 5644, 4888, 3986, 5951, 5271,
              7069, 5559, 7161, 5346, 3701, 6276, 4399, 3538, 7621, 5733, 6101, 5712, 7308, 5927, 7403, 5149, 7950,
              6432, 3594, 7274, 5896, 6295, 6171, 4960, 5053, 4428, 6419, 3417, 4125, 6697, 8323, 3571, 3664, 8070,
              6559, 4694, 5284, 5446, 5764, 2785, 2975, 3667, 4269, 4470, 5004, 5839, 3978, 8241, 4208, 6632, 3709,
              5655, 7774, 8164, 5117, 6529, 3678, 3865, 6667, 8051, 6229, 4442, 6370, 5901, 6742, 3094, 7303, 6133,
              6241, 6236, 6593, 6275, 4184, 3786, 3693, 3730, 6682, 6813, 5955, 3447, 4651, 6696, 4610, 6748, 4975,
              5178, 3470, 3875, 4280, 4762, 7132, 7853, 8260, 7425, 4433, 5135, 5512, 3980, 3317, 4132, 6425, 6033,
              5837, 6787, 3162, 7044, 5445, 3577, 8378, 3784, 6084, 4054, 7721, 5649, 7649, 8145, 6240, 2760, 6101,
              6553, 6594, 8192, 7833, 8259, 6879, 4268, 6485, 3035, 2929, 7814, 4379, 8305, 3211, 4283, 4372, 2906,
              4752, 3727, 5799, 4294, 6296, 4076, 7030, 6167, 4223, 3830, 3372, 2567, 3973, 7073, 4051, 7068, 3835,
              3657, 7178, 5336, 5686, 5436, 3722, 5873, 3264, 5726, 7570, 4069, 4015, 5734, 7208, 6894, 3553, 2780,
              6365, 7071, 6693, 5624, 5017, 5714, 6928, 4440, 7103, 7852, 4384, 6065, 6171, 3396, 4204, 6769, 7680,
              8168, 6276, 3683, 5664, 3477, 7484, 6647, 5616, 4162, 7091, 7949, 4507, 3034, 2887, 7167, 5519, 6532,
              4163, 8028, 6180, 7838, 3364, 4987, 3043, 6121, 5440, 7392, 3426, 6107, 5753, 6936, 8138, 6940, 6480,
              3490, 4335, 2848, 6983, 5150, 3859, 5295, 4398, 6025, 4631, 4886, 5661, 6635, 8203, 7255, 5739, 5478,
              5671, 4605, 4185, 6897, 3638, 2966, 3487, 6774, 6442, 3679, 4170, 6247, 5005, 6677, 4808, 6449, 4313,
              5445, 4789, 4259, 5990, 3785, 4652, 6298, 6650, 7264, 7211, 4873, 5497, 2958, 5489, 7362, 7530, 6536,
              5997, 7114, 6963, 4928, 6600, 3821, 6246, 5673, 6342, 3461, 6019, 2489, 5678, 6048, 4366, 3892, 7494,
              4073, 7220, 5806, 2875, 7951, 5324, 4846, 3662, 5954, 5604, 4028, 5688, 3683, 7066, 5412, 6046, 4755,
              5164, 4044, 5453, 5533, 4646, 2671, 6575, 6555, 4832, 6570, 7992, 4129, 6169, 7399, 3441, 4606, 4603,
              5480, 2823, 3605, 6987, 7427, 4779, 5577, 4449, 4311, 2933, 2554, 2840, 5838, 4087, 7996, 3549, 7372,
              5661, 5370, 7287, 4220, 5153, 4095, 7192, 5400, 4578, 5350, 2481, 6851, 7312, 7278, 8050, 3891, 7391,
              7796, 7396, 7757, 5063, 6305, 3199, 5756, 6406, 6792, 7008, 4337, 3437, 4072, 3537, 7989, 4111, 5580,
              7309, 3476, 5143, 5010, 5885, 7306, 6601, 7045, 6805, 7478, 7153, 2564, 6097, 6994, 5651, 2535, 4702,
              4731, 8004, 5224, 7658, 8056, 3825, 4286, 3486, 7441, 7856, 8053, 4350, 5673, 5200, 5766, 5684, 3406,
              6068, 7374, 3441, 3930, 7106, 3921, 3575, 2870, 4382, 6719, 7190, 5285, 7727, 6418, 5594, 6002, 3274,
              3552, 7157, 5055, 7671, 8034, 4238, 3990, 5554, 3789, 4402, 6307, 8009, 3781, 4955, 6675, 5853, 2894,
              3607, 3363, 4436, 4020, 2936, 3270, 5577, 7556, 4159, 7453, 7193, 5135, 5622, 3591, 8220, 8363, 4440,
              7414, 7772, 6894, 4948, 7230, 6098, 4278, 6392, 4740, 5854, 4238, 3691, 6698, 4283, 5036, 6507, 3387,
              5199, 5833, 7485, 4567, 4715, 5169, 7147, 7242, 4546, 3883, 4222, 7971, 5522, 5948, 4785, 5740, 4009,
              5537, 5319, 5742, 5850, 7358, 6538, 7160, 5765, 3985, 6684, 3311, 7173, 5720, 3641, 3861, 6454, 4538,
              5334, 4003, 5594, 3938, 7464, 3923, 7575, 6818, 7353, 8276, 4836, 4182, 7158, 3724, 7076, 5407, 4874,
              3460, 4486, 5651, 7456, 4264, 5645, 3846, 5432, 6938, 4017, 3874, 3257, 5008, 6572, 6306, 8232, 3830,
              4922, 6039, 2658, 5309, 8007, 5260, 3816, 4935, 4427, 5280, 5458, 7888, 5197, 5619, 6399, 4832, 8194,
              7471, 7414, 8340, 6689, 4862, 7371, 5345, 7352, 6900, 2675, 3917, 4299, 5507, 7118, 7082, 6322, 7333,
              4881, 6795, 5759, 3397, 6457, 4007, 4516, 6850, 5938, 3125, 3941, 8190, 8186, 4299, 3658, 7456, 6691,
              2502, 5349, 4288, 6668, 5548, 3558, 4310, 3313, 3609, 5704, 2597, 3770, 3541, 8281, 6556, 4008, 7521,
              4203, 6796, 4235, 3110, 4857, 5534, 5600, 3703, 2797, 5152, 2682, 6748, 3069, 6876, 7315, 4624, 5701,
              6389, 6010, 3300, 5506, 6713, 3548, 5191, 4736, 2650, 6352, 4884, 3451, 5415, 6575, 6781, 7601, 3845,
              5542, 3072, 7815, 2873, 5875, 5391, 4396, 4147, 4566, 4844, 3657, 7007, 2910, 5996, 4794, 5337, 6616,
              5864, 4858, 3913, 6191, 4801, 5690, 8124, 6897, 5365, 5187, 7204, 5572, 8254, 4210, 6353, 8062, 5081,
              7072, 6200, 2813, 3936, 8174, 6175, 7998, 2558, 4607, 2703, 3417, 7301, 7179, 4709, 2717, 6105, 5386,
              5101, 4918, 5448, 5911, 6000, 4600, 3829, 7913, 7854, 7121, 6250, 2829, 4244, 4063, 6393, 5666, 4080,
              6295, 3871, 5724, 4894, 6511, 8293, 3932, 3508, 4122, 7459, 6355, 5256, 6287, 6273, 5947, 4155, 5508,
              5355, 4127, 8198, 3720, 5757, 3347, 7000, 6134, 3802, 6095, 7467, 2911, 5083, 4908, 3515, 7018, 3351,
              4306, 2607, 5471, 4912, 4894, 6976, 5073, 5085, 4274, 4360, 7041, 6142, 2620, 7516, 3899, 5039, 6600,
              5954, 7466, 4001, 7974, 7415, 3590, 4864, 4474, 4917, 2606, 7329, 6549, 3229, 3390, 3873, 6344, 4357,
              5432, 6100, 7406, 4812, 6612, 3462, 3769, 6411, 5684, 6510, 4569, 5242, 4034, 3807, 8187, 5967, 7294,
              5226, 2648, 6622, 4061, 7314, 6254, 8315, 6928, 4732, 4811, 4749, 3951, 5548, 3611, 5194, 7780, 4958,
              6217, 4211, 6995, 3733, 6311, 3638, 4444, 4613, 7738, 3983, 3700, 5617, 6198, 3492, 3908, 4678, 5182,
              3708, 5870, 6791, 6445, 4254, 4608, 5546, 5552, 2611, 4934, 6448, 4004, 5068, 4670, 3005, 3714, 3986,
              4007, 4626, 6591, 3848, 7554, 6085, 4882, 6495, 6116, 3656, 7312, 8221, 2585, 4134, 7109, 5541, 7273,
              7237, 7067, 6058, 5159, 4827, 6269, 7328, 7635, 5207, 4417, 5074, 3863, 3755, 6139, 6574, 4094, 7193,
              8102, 5812, 6567, 4881, 4766, 5481, 5304, 3661, 4092, 5222, 3423, 4367, 6953, 2789, 7249, 7098, 6968,
              7065, 6741, 5229, 4254, 3375, 6252, 4432, 6684, 7598, 6193, 8346, 5486, 4312, 6550, 6779, 6376, 6674,
              3607, 6272, 7726, 7481, 5991, 5638, 6269, 4463, 3771, 5060, 7215, 7135, 5329, 6146, 6929, 5718, 2878,
              7630, 7473, 7943, 6859, 4144, 3380, 6081, 3111, 4117, 7894, 5404, 7202, 7460, 7057, 5900, 4448, 4712,
              6412, 7048, 5198, 7015, 4205, 7307, 5117, 6415, 7501, 6646, 5855, 5670, 3273, 4107, 6975, 5656, 6092,
              7285, 2550, 5810, 4563, 4964, 4222, 7077, 7646, 6905, 4963, 7956, 7475, 6361, 5906, 6832, 4479, 4285,
              7063, 4186, 4069, 7297, 4711, 4893, 2992, 4137, 8058, 5963, 5052, 5330, 3899, 7532, 5682, 4507, 4937,
              4446, 7387, 8345, 7378, 5101, 6617, 6205, 4639, 3612, 4277, 3202, 4078, 2725, 8253, 5435, 5300, 6271,
              3820, 3579, 6957, 4243, 3922, 5467, 2683, 6324, 7060, 3032, 6118, 4075, 7025, 4911, 5932, 5759, 6883,
              7842, 5747, 4092, 3931, 3403, 2574, 6498, 3540, 3559, 3689, 4501, 6011, 3615, 7144, 6778, 3608, 7083,
              4902, 5597, 3440, 3393, 4563, 6605, 3216, 4392, 5779, 5891, 4660, 6506, 3436, 3870, 6870, 6462, 3838,
              4719, 3118, 4559, 5818, 5908, 6207, 5495, 6749, 6714, 7675, 6628, 5867, 4139, 7285, 4380, 6852, 3632,
              3112, 6144, 5115, 5282, 5665, 3704, 3505, 4175, 4643, 4195, 8320, 6371, 4544, 4386, 4604, 5885, 4616,
              5123, 4522, 7171, 6422, 5363, 7538, 8042, 5511, 7745, 4410, 5444, 3886, 7254, 6368, 7789, 5386, 4316,
              3813, 6608, 7786, 7077, 4018, 7100, 6623, 4540, 6242, 4307, 6838, 5817, 6776, 2595, 6375, 3819, 7401,
              5000, 3639, 2932, 6562, 6823, 6681, 7571, 6238, 5336, 6710, 3449, 7724, 5609, 5479, 4562, 3962, 4240,
              7896, 7301, 4891, 7710, 4318, 3692, 6352, 8362, 6353, 7375, 6715, 3751, 6642, 3837, 5358, 3434, 5685,
              3681, 5844, 3315, 6569, 5287, 3949, 3465, 6842, 4817, 3674, 7204, 4544, 6162, 5975, 8049, 3534, 5010,
              5472, 3939, 5680, 4619, 4625, 5298, 5162, 6126, 4592, 5500, 7433, 7320, 3321, 2524, 8057, 7980, 6259,
              6742, 5009, 2496, 2493, 7038, 3879, 4764, 5892, 4787, 4332, 5072, 4650, 6288, 6301, 4706, 6793, 6403,
              7184, 2769, 5177, 7822, 4752, 7129, 4014, 6758, 6168, 7105, 3496, 3466, 5755, 3438, 6035, 3054, 6323,
              4171, 6314, 5288, 4958, 4818, 4488, 4399, 6465, 3373, 5567, 7832, 5866, 7023, 7298, 4470, 7690, 5293,
              5786, 3608, 6154, 2581, 7669, 2482, 5054, 4272, 7235, 8064, 5071, 7465, 5668, 7863, 6558, 4043, 6737,
              5160, 7589, 5327, 3424, 8267, 5877, 6527, 7477, 2982, 3988, 6994, 5352, 4279, 4527, 5778, 6628, 6656,
              4698, 3911, 3263, 3658, 7404, 5586, 3528, 5250, 8330, 2575, 3926, 3769, 4607, 6811, 6424, 4428, 3642,
              7886, 3915, 5494, 6505, 5305, 4785, 3946, 5456, 6786, 4710, 6441, 2582, 5409, 7529, 4355, 6577, 3516,
              7040, 5324, 7099, 6563, 5449, 5574, 4393, 6902, 8233, 5602, 7731, 4024, 5776, 5655, 6626, 6688, 4622,
              6856, 3194, 4586, 2917, 3550, 6767, 7335, 3659, 5739, 5422, 5930, 4834, 6237, 5319, 5363, 6775, 5847,
              2571, 6433, 3973, 5014, 4249, 6417, 4298, 2860, 3774, 4231, 6754, 7012, 4639, 3595, 4381, 3897, 5912,
              5964, 3858, 5848, 7488, 6740, 6337, 6657, 3656, 6448, 6609, 3600, 3030, 5179, 3602, 3527, 3517, 4663,
              6197, 4367, 6137, 5220, 5650, 6640, 4003, 5401, 3543, 3222, 3223, 4761, 6141, 4554, 7754, 3745, 2561,
              6057, 3547, 7470, 4313, 6266, 6659, 6988, 8067, 6943, 6120, 5374, 4619, 6838, 6299, 2844, 3465, 7107,
              3190, 4297, 3969, 3984, 6227, 5805, 7957, 4521, 6144, 7775, 8248, 6497, 5710, 3467, 7095, 5582, 3474,
              4073, 7034, 5137, 2926, 5232, 5769, 7235, 2678, 8060, 6638, 7183, 7728, 6149, 6680, 4620, 7633, 6251,
              6772, 4115, 7261, 5879, 6794, 4897, 3339, 5420, 6964, 5419, 3595, 5648, 8103, 7602, 4156, 6888, 7338,
              2920, 4483, 2988, 7402, 5578, 4341, 4176, 3717, 4741, 2559, 7175, 4869, 7893, 7549, 3709, 8321, 7039,
              6568, 3738, 4306, 4664, 3582, 5176, 2631, 3870, 6957, 8033, 4939, 7569, 5846, 5215, 7611, 3533, 4891,
              3198, 7122, 4408, 5914, 3814, 6901, 4165, 2804, 8329, 4733, 6708, 5539, 7522, 5934, 3127, 7137, 5270,
              7163, 2763, 4325, 5248, 7317, 8219, 4951, 2534, 4265, 4056, 5907, 2721, 6291, 5537, 3078, 5321, 4091,
              7303, 4197, 8040, 7190, 7033, 5542, 3782, 8052, 7920, 5308, 5232, 5570, 7126, 4406, 2478, 7157, 7749,
              6996, 4340, 6954, 3448, 4352, 4185, 5513, 3778, 4279, 3706, 3680, 5820, 4631, 3579, 2477, 4510, 5705,
              6029, 4839, 4982, 2907, 5111, 7827, 7805, 6436, 3515, 5241, 2744, 6701, 5895, 3645, 6287, 3429, 4600,
              4265, 6222, 4031, 5663, 5049, 4896, 6643, 6396, 2691, 4906, 7423, 3142, 8091, 3482, 3490, 3587, 3509,
              6654, 6903, 8367, 2752, 5284, 7504, 6321, 8344, 6619, 2861, 7509, 4840, 8213, 6093, 4508, 6803, 2480,
              6918, 3697, 6052, 4537, 4138, 3785, 8155, 6862, 4506, 2547, 5356, 4671, 2981, 4221, 3480, 4835, 6835,
              6989, 5076, 6680, 2720, 4896, 5372, 7947, 5562, 7246, 4922, 4845, 7215, 4581, 3735, 6374, 4029, 3426,
              3922, 5046, 7144, 6045, 4338, 5635, 7993, 2560, 2565, 4791, 5898, 5032, 8354, 7729, 8316, 4761, 7013,
              3039, 3712, 4484, 5414, 3907, 6692, 6163, 4079, 7403, 4369, 8151, 5018, 2660, 5040, 2718, 7871, 6321,
              6590, 3358, 7229, 7413, 5950, 4052, 4779, 6060, 6886, 5616, 6839, 3288, 3991, 6849, 3384, 5492, 6581,
              6300, 3575, 7010, 8271, 7027, 5687, 5882, 3708, 8142, 7236, 3598, 5545, 4929, 8030, 5893, 4468, 6220,
              3869, 7844, 7514, 4919, 7135, 3550, 4797, 6488, 2537, 3649, 5393, 3762, 5001, 5091, 5482, 5551, 5789,
              5026, 7379, 7271, 5226, 7115, 4503, 6475, 2825, 3442, 8162, 3984, 5948, 5452, 4802, 5388, 7812, 5722,
              5493, 3458, 4076, 5959, 3433, 7148, 7115, 7260, 8041, 6668, 5003, 5227, 7342, 3232, 7779, 5113, 5273,
              7623, 6806, 3406, 7412, 8238, 7595, 3269, 6289, 3900, 7628, 4590, 6703, 7319, 4501, 5411, 6284, 4584,
              4548, 6500, 7189, 4629, 7284, 3196, 6765, 5104, 3763, 7452, 4138, 6251, 4613, 5481, 6456, 6449, 7610,
              7087, 7697, 3275, 3446, 6726, 5590, 6614, 4400, 6931, 6689, 3083, 3713, 4703, 7438, 4744, 4355, 4027,
              5985, 8143, 6896, 5503, 5913, 4848, 4728, 3068, 6497, 3584, 6440, 6354, 6657, 4512, 5990, 7126, 5953,
              7398, 3843, 6081, 4642, 4901, 7130, 7437, 5109, 8177, 6861, 6517, 3705, 2885, 6690, 3404, 4493, 6825,
              7934, 3578, 7295, 7659, 7393, 5071, 5255, 4998, 5325, 6791, 5752, 3659, 2588, 3954, 5215, 3049, 7343,
              5305, 6867, 4511, 3942, 3180, 2783, 7146, 8128, 5768, 3130, 4020, 5437, 7872, 6818, 3753, 6511, 5790,
              4130, 8229, 4429, 7164, 6318, 4880, 7093, 8325, 2951, 4484, 7580, 3381, 6611, 4707, 5518, 5487, 4093,
              3539, 2786, 3439, 5434, 6045, 6484, 8365, 2666, 5664, 4865, 5599, 4070, 4315, 4575, 5156, 5870, 3203,
              3942, 4560, 3757, 2968, 6341, 5389, 4358, 7508, 4040, 5261, 4213, 5524, 6636, 5865, 7326, 6782, 5720,
              3386, 7050, 6006, 5694, 3233, 3286, 7139, 7376, 3834, 6521, 3810, 4237, 6429, 4823, 8251, 3402, 3633,
              5540, 7449, 3670, 3230, 3957, 7746, 7110, 6552, 2507, 7378, 5464, 7211, 7213, 5730, 7202, 4952, 5466,
              7472, 4305, 5168, 7139, 6234, 3415, 7892, 7334, 6258, 6169, 7695, 5036, 4098, 7899, 6840, 6823, 6599,
              5523, 7331, 4798, 3484, 6686, 4123, 5281, 5233, 4529, 8286, 6884, 7185, 3544, 5706, 5880, 6208, 6891,
              4255, 7072, 4085, 7439, 5929, 5549, 7199, 7468, 5539, 2827, 4495, 7693, 6942, 5893, 6041, 8243, 3297,
              5707, 7058, 6436, 3471, 5186, 4680, 5490, 4598, 6459, 5547, 6682, 4987, 3817, 5515, 3880, 3631, 5791,
              6161, 6942, 3647, 7816, 3294, 5183, 4804, 4612, 6135, 4456, 7197, 4796, 8246, 3860, 5636, 5891, 3025,
              7241, 7562, 7249, 5957, 8095, 4443, 4850, 7385, 8012, 7608, 4695, 4528, 5615, 5463, 3650, 4410, 4548,
              7349, 5934, 5051, 5099, 8099, 2699, 6490, 4052, 3551, 4615, 5296, 6747, 7280, 8005, 7253, 6059, 6494,
              2841, 7567, 6483, 5127, 6542, 8024, 3827, 7300, 4332, 4104, 4644, 6784, 6290, 8129, 6413, 2479, 4258,
              6564, 4687, 4016, 4344, 5505, 4071, 3434, 7084, 4084, 4473, 5069, 4813, 4640, 7967, 8163, 8257, 6993,
              4033, 3500, 6131, 5058, 6788, 3520, 7469, 3462, 4750, 8266, 4666, 7018, 5223, 5866, 2643, 4136, 4362,
              5897, 3665, 4523, 5434, 6508, 6091, 3359, 5888, 4553, 5350, 3893, 6939, 4454, 4573, 4359, 4933, 6810,
              3533, 7421, 7075, 6624, 3469, 7073, 4196, 3894, 5264, 4291, 8152, 7118, 7470, 6333, 6723, 8080, 7089,
              6603, 4750, 4260, 3291, 3865, 4256, 7526, 6577, 6736, 5971, 6756, 2937, 2583, 3520, 6482, 4800, 4710,
              7417, 4151, 7081, 4089, 7219, 4816, 6388, 3700, 6596, 7178, 3061, 7813, 5451, 5709, 7351, 2908, 4415,
              6758, 6837, 3838, 7540, 7381, 3648, 3646, 3552, 5625, 6071, 4515, 5190, 4909, 6876, 4376, 6694, 7305,
              6579, 4273, 7291, 5886, 6476, 4699, 3816, 4758, 4062, 3743, 5693, 5429, 6220, 3920, 6466, 4395, 3772,
              6895, 3409, 5758, 3780, 7049, 4036, 7054, 4945, 7588, 3453, 7436, 4973, 6814, 4869, 4186, 7986, 3388,
              6027, 4806, 8167, 7150, 5815, 4371, 7637, 5269, 3968, 7489, 4812, 7017, 2930, 7316, 7084, 7341, 5695,
              7480, 6655, 7692, 7678, 3455, 3793, 3905, 5067, 3530, 6761, 7327, 4483, 7203, 6015, 5916, 7128, 7902,
              3646, 7735, 4579, 5989, 5040, 7732, 4498, 4250, 6710, 4821, 3934, 7228, 3750, 6960, 2754, 4060, 3691,
              6926, 5133, 6260, 5634, 6080, 7339, 7339, 7582, 3893, 7431, 4696, 3546, 6157, 6041, 4595, 5288, 4415,
              2750, 5416, 3581, 4633, 4218, 4822, 5044, 4373, 4191, 6544, 7577, 7245, 5231, 3122, 3510, 7350, 4890,
              6652, 6111, 4141, 5970, 4042, 5668, 5180, 3371, 5971, 5087, 7283, 3517, 4729, 3518, 4346, 4588, 6966,
              3502, 4017, 4687, 5026, 5977, 7673, 6589, 2778, 4576, 6624, 3402, 5614, 8207, 4670, 5563, 3622, 5351,
              5102, 5313, 5830, 3026, 6793, 2636, 8149, 6320, 4213, 6161, 4334, 6064, 6486, 6384, 4672, 5666, 7142,
              5683, 7441, 7078, 5473, 7276, 5798, 4945, 5912, 3803, 5211, 5939, 6635, 4444, 4259, 5105, 3505, 4611,
              6137, 8374, 3184, 4509, 3674, 5421, 6122, 7767, 5438, 5760, 2625, 3344, 4150, 7639, 2637, 5595, 2634,
              6699, 4568, 6113, 6591, 6683, 6539, 7806, 4413, 6076, 6427, 4431, 5533, 7261, 6861, 7406, 6172, 6026,
              4112, 3303, 7946, 5140, 6421, 8105, 8109, 4552, 6669, 7368, 7087, 3431, 4036, 6777, 3839, 6189, 6317,
              4570, 5102, 7859, 7586, 5520, 6948, 6189, 5152, 3323, 6475, 3220, 4460, 7583, 5732, 7429, 4204, 3977,
              6808, 6192, 3416, 6229, 4386, 7168, 4350, 7559, 4997, 4488, 5910, 6810, 7862, 4493, 7330, 3588, 3422,
              6016, 4048, 6226, 6596, 3812, 4511, 5298, 5778, 5786, 5847, 5136, 5593, 5962, 4578, 4961, 3016, 4855,
              4574, 7143, 3561, 4347, 5362, 2741, 6654, 7447, 2965, 5657, 4632, 4049, 3940, 5698, 3583, 4683, 5127,
              3800, 6667, 6248, 3428, 3028, 7373, 3526, 4558, 6042, 5856, 3504, 2483, 5985, 8348, 2969, 5966, 4860,
              7590, 2661, 7468, 5803, 7880, 7195, 4301, 4763, 3982, 6773, 6789, 5745, 4875, 4876, 7981, 3414, 4562,
              8130, 3532, 6234, 5480, 5186, 5841, 3904, 3392, 4592, 7960, 5381, 3654, 3904, 5633, 6416, 7811, 6402,
              5703, 8069, 2954, 3606, 4641, 7302, 3006, 5749, 4954, 7058, 7316, 5155, 3902, 6573, 2925, 4662, 3224,
              6054, 3285, 6551, 7112, 2601, 7752, 5258, 6486, 4614, 7849, 6581, 5070, 7102, 3590, 8382, 5210, 3970,
              7942, 7877, 7269, 3066, 8263, 3717, 5050, 6008, 6339, 5077, 5292, 4114, 3668, 4305, 4148, 3824, 3628,
              3565, 3187, 7860, 2774, 5817, 2833, 4827, 4583, 2520, 5006, 3204, 3808, 6828, 6163, 7694, 6799, 4308,
              5311, 6815, 5321, 3966, 6537, 4721, 4780, 4682, 4360, 6845, 7429, 6179, 6548, 6078, 6526, 4292, 3759,
              6584, 4840, 3478, 6460, 6046, 4730, 4591, 2838, 7167, 6976, 6743, 2761, 7032, 5499, 5875, 6771, 3645,
              8158, 5724, 6445, 6516, 6716, 6335, 5558, 3967, 4541, 4174, 6604, 7070, 6458, 5963, 5064, 4485, 3440,
              5531, 4961, 6315, 4329, 5378, 4571, 4708, 6380, 7138, 3908, 3797, 3756, 7593, 4209, 6195, 6880, 6470,
              6565, 7997, 5966, 7765, 6545, 5175, 4023, 8081, 8073, 6055, 6327, 5748, 6618, 5082, 6551, 3464, 7059,
              6956, 4835, 6159, 5609, 6893, 3997, 3397, 3075, 6639, 7867, 4039, 3652, 6108, 2734, 7138, 2942, 2474,
              5098, 4883, 3139, 6583, 4652, 4754, 6969, 7401, 4609, 5800, 6158, 3975, 3268, 3419, 2676, 6463, 6130,
              6238, 8169, 6905, 6072, 3161, 5979, 5857, 2892, 3761, 7620, 5492, 2756, 2531, 4342, 6775, 3619, 6973,
              5159, 3818, 3766, 4729, 6715, 6147, 6109, 2627, 6697, 4263, 4565, 5264, 6062, 4911, 5151, 5681, 4535,
              8357, 5315, 4596, 4821, 4941, 7242, 3862, 4885, 4582, 4166, 4411, 4328, 6896, 6007, 6382, 6954, 6289,
              5949, 3603, 5131, 4775, 3696, 7177, 5460, 6381, 6072, 8098, 6821, 5261, 5014, 6129, 5195, 6538, 7510,
              2610, 6782, 7864, 5797, 2795, 5958, 7632, 6194, 7747, 3748, 4391, 7469, 5424, 2598, 3408, 4589, 6821,
              4206, 6555, 7546, 7386, 6535, 5378, 7552, 3280, 4702, 4530, 4281, 6181, 4914, 5245, 8249, 5183, 3857,
              3854, 5626, 4587, 6054, 4216, 3619, 3613, 4074, 4000, 4219, 4533, 5552, 5415, 3121, 6705, 4239, 3948,
              6687, 4293, 8076, 6394, 7014, 6086, 4043, 6086, 7079, 5486, 6950, 4407, 6356, 4830, 4966, 2997, 6277,
              2912, 2897, 6421, 4261, 4864, 5680, 3430, 3143, 4909, 5835, 6803, 4224, 4065, 3900, 2724, 3648, 5568,
              4426, 6917, 4813, 7238, 7223, 6467, 5660, 5956, 3910, 2921, 4464, 4694, 4688, 5850, 6396, 4167, 6909,
              5367, 5328, 7309, 4697, 6372, 6230, 3841, 6509, 3524, 7148, 4342, 5592, 7351, 5792, 7369, 8137, 5235,
              7306, 4193, 8381, 5202, 8020, 3979, 4135, 7212, 8117, 4187, 4388, 5251, 5353, 7164, 3632, 4976, 2555,
              5289, 5174, 6921, 4524, 3064, 4374, 6473, 6239, 4899, 6485, 3996, 4033, 5992, 4315, 5395, 6491, 5880,
              3265, 5093, 4948, 3569, 3398, 7758, 4387, 7962, 8043, 5418, 6746, 3995, 7036, 6277, 2940, 7709, 6383,
              7155, 7761, 4414, 6225, 5467, 8038, 4489, 5620, 5409, 4054, 4933, 7428, 4545, 7397, 3031, 4311, 8008,
              6883, 5732, 2845, 4641, 4058, 5265, 4220, 7926, 4269, 4965, 2781, 4689, 4838, 2775, 7642, 4131, 4672,
              6852, 6450, 6384, 3775, 6124, 5012, 4943, 5302, 6533, 7383, 7652, 3760, 2864, 6235, 2952, 8121, 5099,
              5362, 5980, 3950, 4695, 6319, 7890, 6439, 3834, 7123, 6766, 7124, 6847, 3703, 5562, 5924, 5979, 4760,
              3890, 4097, 6598, 4173, 7785, 4547, 7111, 4932, 5930, 6119, 7347, 5984, 2591, 3774, 4435, 6847, 6745,
              3594, 6670, 5768, 2546, 4114, 2697, 3666, 7706, 5859, 3919, 3650, 7446, 3087, 6539, 4980, 2527, 5757,
              5998, 6350, 5813, 5583, 2713, 5233, 6616, 4392, 6817, 2653, 6422, 5283, 5161, 7162, 4383, 6856, 5431,
              7756, 8212, 4895, 5498, 3815, 5929, 7158, 4580, 5897, 5328, 5921, 3676, 6170, 5946, 3336, 7174, 5080,
              4422, 3967, 6787, 7040, 7991, 5410, 2593, 5939, 5338, 2513, 8134, 4602, 6806, 7969, 4931, 7773, 2632,
              5809, 5675, 6519, 7153, 3779, 6764, 4113, 6991, 6816, 7064, 5247, 8088, 6797, 5982, 6841, 6704, 3261,
              4390, 7279, 5614, 6961, 6022, 7396, 7237, 8172, 4649, 4352, 3811, 4424, 2543, 5864, 6526, 4830, 3866,
              8349, 5576, 2751, 7499, 6981, 8301, 3084, 5825, 8296, 5129, 7218, 6730, 4543, 2562, 5859, 5652, 7263,
              6904, 4657, 6695, 7269, 6151, 6576, 3970, 6914, 4271, 3695, 6641, 7191, 6004, 6804, 6766, 2579, 5936,
              3924, 6571, 6725, 6633, 5161, 6364, 8364, 2592, 3512, 7355, 3895, 6128, 6629, 5125, 3726, 7876, 4058,
              5379, 4654, 2573, 6988, 7268, 6502, 5620, 6118, 4764, 6542, 6939, 5766, 5361, 5974, 8309, 4597, 5268,
              7835, 6924, 4693, 3852, 5093, 3418, 5507, 6990, 6826, 4625, 2948, 2843, 5872, 4765, 4716, 5051, 8114,
              3853, 5020, 3419, 3998, 6138, 3643, 5714, 3570, 6460, 7818, 4627, 8333, 3177, 6598, 4951, 4980, 4437,
              5167, 6563, 8255, 6528, 5715, 4825, 3038, 3504, 4550, 6241, 4170, 4550, 2486, 3587, 7225, 2866, 6712,
              8331, 5607, 5351, 5151, 7416, 4284, 5097, 4172, 5471, 2670, 5463, 4757, 7581, 6796, 7370, 3478, 5566,
              5265, 4478, 7145, 4412, 5819, 7288, 3529, 4012, 5211, 3555, 2639, 8001, 2514, 7002, 6671, 5730, 7166,
              2820, 6621, 4331, 5340, 4727, 7020, 4391, 4031, 3742, 5477, 3696, 3655, 3670, 5218, 5721, 5132, 5116,
              7553, 4235, 2635, 5184, 6279, 6698, 8027, 6700, 8196, 6927, 7451, 4734, 3929, 8183, 6724, 6830, 5322,
              7057, 3602, 2805, 5043, 3523, 6017, 5677, 3882, 7232, 4635, 4038, 7783, 5631, 5416, 4680, 6009, 3918,
              5187, 6166, 7560, 5339, 6974, 5347, 5496, 5254, 7407, 3936, 3633, 7476, 7739, 4863, 6705, 5792, 7227,
              5520, 5632, 7664, 6219, 2677, 6286, 3614, 2839, 5085, 6314, 2654, 5674, 6843, 6042, 6619, 7663, 7881,
              2501, 6936, 7901, 7299, 7836, 8029, 5660, 3459, 6192, 7194, 3172, 5586, 5122, 5669, 4442, 5561, 5125,
              3763, 7172, 6944, 5642, 5514, 4120, 4982, 8066, 4296, 3616, 5972, 5119, 3994, 3925, 6068, 5871, 6293,
              6298, 5662, 7495, 4616, 4327, 6087, 6819, 7003, 3978, 3560, 5451, 5137, 5243, 4770, 3387, 7145, 4356,
              5035, 6922, 4047, 5799, 7074, 4609, 6242, 6261, 6028, 6595, 5095, 5855, 5672, 3545, 4101, 5037, 5108,
              7861, 2621, 6096, 6502, 8366, 4401, 7383, 3940, 3318, 2541, 5349, 4530, 4453, 4880, 4405, 3731, 6620,
              3479, 3116, 6186, 7828, 5502, 4946, 3622, 4520, 7163, 6007, 6414, 6129, 7344, 3930, 6651, 4319, 6862,
              5961, 3861, 5733, 4498, 3710, 5794, 3842, 5385, 3777, 5068, 4748, 6408, 5909, 4178, 6259, 7821, 6210,
              3835, 6865, 5726, 7085, 6585, 4041, 6666, 7883, 7180, 4095, 7433, 6556, 3549, 6185, 5143, 7918, 6565,
              8343, 7275, 3237, 5250, 5483, 5333, 3459, 5437, 5343, 7213, 2553, 3840, 5940, 4904, 7066, 5338, 5628,
              4463, 4477, 2776, 5931, 5935, 3921, 3538, 4365, 4930, 5705, 7605, 3781, 4133, 8361, 5568, 6452, 6431,
              4237, 7022, 7310, 4868, 7382, 6605, 5965, 5510, 5047, 6196, 2964, 5518, 3767, 5206, 6916, 3108, 4605,
              3762, 4706, 4786, 6783, 4021, 4339, 8227, 6390, 4648, 5292, 6701, 5120, 3425, 4194, 2998, 3019, 5345,
              2505, 3690, 3651, 5816, 6050, 5740, 8059, 5314, 5807, 2842, 4290, 3144, 6418, 4727, 4223, 5086, 5393,
              5116, 5069, 6185, 4449, 4941, 7034, 8179, 3903, 2859, 3327, 2768, 3437, 8185, 5860, 7430, 7292, 5650,
              3098, 6741, 4995, 3593, 4471, 4743, 4673, 5928, 4253, 7999, 3106, 3641, 5902, 3812, 7723, 6848, 6200,
              7958, 7705, 3989, 4859, 8118, 6756, 3102, 4898, 6744, 8176, 6670, 5033, 7359, 5315, 2526, 7228, 8035,
              3727, 3617, 5184, 6869, 5772, 7231, 3722, 5804, 7462, 6672, 8250, 4001, 4000, 7399, 5962, 5309, 3466,
              2949, 3964, 5843, 4275, 4421, 7356, 5725, 5641, 3988, 3443, 6031, 6588, 4998, 4280, 4339, 4624, 5438,
              2935, 2723, 5242, 6109, 5895, 7377, 5460, 4369, 3369, 5134, 3555, 4189, 4598, 4675, 3729, 4011, 5721,
              2589, 3850, 6398, 3728, 2731, 8205, 7793, 8204, 4006, 6580, 5876, 5296, 6979, 2519, 7819, 4061, 7388,
              5286, 4464, 8270, 3671, 3242, 6434, 7380, 7681, 6024, 3599, 4513, 6585, 6544, 7080, 4859, 4682, 5329,
              4637, 3015, 2735, 6971, 7079, 3209, 7024, 4219, 2568, 6305, 6997, 4773, 3003, 5306, 4230, 4543, 7346,
              6786, 4988, 5262, 6890, 4962, 7266, 4590, 7388, 5603, 5156, 5114, 3805, 6406, 4791, 5544, 6407, 5267,
              4316, 3556, 5496, 3663, 6663, 8157, 4650, 6261, 6446, 3512, 6974, 5234, 6809, 4189, 3495, 7258, 4553,
              3093, 6369, 5355, 6751, 7666, 4734, 6256, 4759, 3488, 4984, 8002, 4074, 6644, 5008, 4612, 6376, 7216,
              6464, 5969, 6328, 4034, 6351, 3692, 4621, 3215, 5728, 5247, 4940, 4084, 6244, 6877, 7563, 7931, 5303,
              5603, 4430, 3667, 7446, 2802, 3953, 3620, 3976, 7127, 3689, 7180, 5629, 4819, 6456, 5619, 6343, 2673,
              3669, 3846, 7904, 4139, 3744, 7915, 7689, 5989, 6882, 7056, 4782, 5964, 5056, 3186, 3422, 8000, 6364,
              2711, 6034, 7584, 6908, 4976, 5980, 5357, 5335, 3085, 7437, 4768, 5944, 4040, 8258, 5267, 3159, 6252,
              3976, 3124, 6771, 3427, 3991, 4345, 6148, 6557, 6878, 2922, 4777, 2956, 4567, 3688, 5981, 4198, 6253,
              3836, 4291, 5020, 3996, 4972, 5957, 5454, 4194, 6338, 3862, 6754, 7906, 3409, 2557, 6559, 6859, 3167,
              2536, 4565, 7418, 3916, 3559, 8072, 6507, 5395, 4389, 4927, 4983, 5790, 6282, 5973, 5239, 6067, 8223,
              4211, 7030, 5348, 4771, 6056, 5538, 4833, 5916, 6216, 2941, 3980, 7402, 4109, 4086, 6145, 3090, 8044,
              3081, 4995, 4681, 7244, 5591, 3166, 7830, 3349, 2668, 7640, 4320, 5511, 4221, 4560, 7539, 7777, 7393,
              5803, 6927, 6874, 3073, 5598, 4669, 5043, 4569, 3747, 6949, 4784, 4959, 4588, 4372, 7345, 4649, 5405,
              5421, 5777, 5392, 5834, 4831, 5524, 5947, 6762, 6889, 4467, 4450, 3990, 4753, 4738, 2984, 6548, 4064,
              6477, 5073, 6640, 5883, 7599, 3542, 4096, 3256, 3024, 5331, 5356, 5262, 5902, 4594, 3378, 3719, 2777,
              5493, 3328, 7231, 3951, 5590, 6461, 5212, 7381, 2886, 5687, 4502, 5861, 5045, 7002, 3906, 4340, 8101,
              6215, 4495, 2686, 4946, 3809, 7622, 6285, 7515, 7670, 5925, 5275, 5993, 4847, 6117, 6090, 4893, 5554,
              5824, 6484, 6102, 3056, 6150, 6283, 3000, 3277, 7434, 7966, 3481, 2742, 7186, 6970, 6215, 5325, 2972,
              6561, 4810, 4528, 5649, 6908, 3711, 4363, 4454, 4343, 5788, 3430, 2509, 5526, 7394, 6490, 6925, 7935,
              3506, 5851, 2488, 2630, 3852, 4591, 3681, 7226, 4171, 3928, 5686, 6625, 6212, 3736, 6450, 7152, 7029,
              5272, 5406, 4766, 5860, 7043, 7457, 4281, 4128, 8216, 4397, 4972, 4845, 3322, 8085, 4692, 3910, 6199,
              5358, 5166, 7845, 8247, 6752, 5625, 4100, 7324, 8006, 5370, 3773, 3664, 7071, 5899, 7715, 4986, 6508,
              4457, 6547, 4749, 2633, 2664, 7021, 3864, 4967, 7159, 4295, 5443, 4155, 7092, 6038, 5592, 5589, 3746,
              7425, 4293, 6013, 6952, 4207, 5420, 5881, 4055, 5945, 5259, 2801, 4996, 6089, 6826, 5728, 7472, 5455,
              3301, 4504, 6349, 3119, 4282, 4232, 3933, 6599, 5268, 5484, 5942, 6447, 7568, 7655, 3489, 6696, 4718,
              6513, 7636, 7324, 4437, 3983, 6659, 6156, 6043, 3284, 5303, 5015, 7444, 7055, 4772, 4538, 4284, 6937,
              7357, 3682, 4645, 6738, 6307, 5155, 4763, 4690, 4955, 7511, 4593, 6809, 6573, 7281, 4462, 5079, 5716,
              7787, 5459, 3591, 5968, 5317, 4584, 4456, 3635, 6871, 3876, 7411, 3404, 3502, 4770, 3500, 7360, 6174,
              8089, 5754, 6075, 4532, 6033, 4064, 3483, 4690, 5729, 3553, 6281, 6213, 4234, 4927, 3305, 6898, 7417,
              7233, 5398, 4735, 3308, 7431, 3450, 7283, 6474, 5465, 7988, 6966, 4197, 5062, 3150, 4476, 5030, 7454,
              3499, 4427, 6112, 6541, 2517, 3137, 5042, 7321, 4992, 6381, 4816, 6249, 6644, 5627, 5769, 7645, 5147,
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              2494, 5497, 4696, 7133, 5845, 7293, 8200, 7110, 4274, 6986, 2506, 7662, 5244, 3818, 4805, 4163, 7561,
              5304, 4699, 2877, 3018, 2884, 7086, 7497, 6514, 7259, 3337, 4097, 2626, 3761, 6268, 7348, 6781, 2628,
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              6630, 6202, 2655, 7289, 5525, 5719, 7121, 5796, 6764, 5457, 7629, 7443, 5804, 7111, 8355, 6576, 5427,
              4267, 8230, 4964, 4903, 5057, 5146, 6982, 5723, 3875, 5634, 4365, 2947, 4267, 6466, 7246, 4633, 7759,
              7961, 8144, 4188, 6594, 7038, 7857, 7172, 6602, 4167, 4999, 7161, 6327, 7257, 3583, 3033, 4673, 4430,
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              7031, 4971, 6888, 5700, 5615, 8175, 7395, 3367, 4471, 6386, 7252, 4798, 6985, 3968, 6827, 6561, 6785,
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              6240, 3856, 4331, 7295, 6798, 7166, 4161, 2828, 5585, 7458, 5177, 3752, 2881, 4704, 7519, 5842, 6795,
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              4938, 6400, 6583, 3673, 7606, 7203, 3914, 7311, 2791, 4091, 6387, 2672, 6231, 5147, 7948, 6884, 7638,
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              5446, 4395, 4632, 4480, 3887, 7520, 4510, 8018, 4878, 6366, 4572, 7325, 5006, 6079, 7086, 5180, 4420,
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              3800, 4959, 3750, 5901, 4461, 6278, 6535, 6223, 6613, 3902, 5711, 6959, 4659, 6393, 5383, 5431, 5637,
              6816, 5618, 8123, 4899, 4792, 4879, 5387, 4309, 5134, 3939, 6846, 6557, 2604, 7188, 4939, 6332, 7753,
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              4630, 5249, 3239, 3711, 6239, 5585, 6323, 2612, 5107, 5191, 4684, 7068, 5735, 7194, 6491, 3095, 7274,
              3676, 7428, 5320, 2605, 4361, 5821, 4448, 6359, 3872, 7426, 3620, 4181, 7566, 4714, 5752, 4045, 5150,
              3491, 5953, 7483, 4847, 6446, 6365, 5002, 5621, 7342, 7205, 5016, 3600, 3530, 3793, 4261, 7046, 3828,
              8284, 3292, 5030, 3022, 6920, 5217, 6949, 3884, 5024, 2629, 6304, 6177, 2973, 3152, 3925, 6047, 5384,
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              4634, 7683, 3473, 5322, 5075, 7976, 5841, 8285, 7982, 6933, 5374, 4435, 7837, 6209, 5246, 5973, 5873,
              4936, 6722, 2600, 4089, 2826, 4949, 4707, 4732, 6105, 5862, 7928, 6219, 8093, 6433, 8338, 4262, 6564,
              2874, 4144, 8161, 7116, 4753, 4258, 4757, 7648, 4055, 6662, 3405, 7730, 2705, 5863, 6512, 7181, 3051,
              4093, 5854, 7448, 7444, 6428, 5417, 5394, 7013, 5919, 5013, 6678, 3238, 3442, 8262, 2748, 5927, 5464,
              3713, 7459, 4397, 4620, 2552, 4421, 5876, 7462, 4433, 7039, 4086, 3945, 7650, 6363, 3508, 6132, 6637,
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              5581, 6892, 7259, 7525, 6671, 7493, 4384, 4582, 4524, 4077, 5530, 3725, 5333, 7909, 5658, 6784, 6566,
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              7243, 6779, 6733, 7419, 6606, 6423, 7719, 5418, 6111, 6857, 5334, 5082, 4969, 7443, 4525, 7263, 5643,
              7445, 5469, 7937, 6175, 7985, 8014, 6348, 8025, 5373, 6547, 5078, 3873, 6139, 4800, 3868, 3488, 4288,
              6413, 4537, 3784, 5212, 5709, 2849, 5605, 4534, 6309, 3728, 5132, 6804, 2533, 3266, 4005, 5179, 5643,
              5961, 3618, 4338, 8287, 5202, 4771, 5331, 4289, 4575, 4796, 7808, 7848, 4356, 3283, 6960, 5281, 4853,
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              7744, 4272, 3565, 7210, 4301, 4728, 6987, 6176, 5485, 5617, 6187, 5045, 2846, 3729, 2991, 5699, 6473,
              7426, 3626, 3535, 7273, 3730, 4606, 3788, 7384, 5145, 7134, 3783, 4137, 3804, 8383, 2532, 6401, 6193,
              7081, 5981, 6773, 3262, 7369, 5612, 6874, 4660, 6211, 5225, 7290, 3115, 3637, 4200, 7345, 7186, 4216,
              3060, 5976, 3463, 7289, 2696, 4321, 8313, 5403, 6049, 5883, 6444, 6188, 6797, 4255, 4705, 7458, 2715,
              6807, 3299, 6536, 6959, 7108, 6074, 6946, 3739, 2879, 4751, 2709, 6249, 4679, 6805, 4936, 5522, 3993,
              6482, 7314, 5640, 4304, 6377, 3630, 3963, 6336, 2540, 6428, 2986, 5433, 7916, 4999, 6665, 7665, 4250,
              5707, 8173, 6993, 6729, 7438, 5679, 4110, 7362, 7984, 7536, 7337, 5800, 5275, 5877, 5207, 7281, 5299,
              3792, 2971, 5685, 3477, 4378, 5581, 3694, 8324, 5605, 3799, 7296, 2915, 5382, 6492, 3423, 4923, 6899,
              7771, 4019, 6283, 4747, 4432, 8353, 4691, 2977, 3131, 5110, 3949, 4920, 6978, 4257, 6398, 8208, 7545,
              4345, 7708, 5465, 4217, 7047, 5205, 4983, 7320, 8195, 6869, 4351, 3412, 6203, 4188, 4122, 4970, 6540,
              8278, 4227, 6721, 6021, 6828, 6153, 3747, 3578, 4026, 4789, 5819, 6265, 2891, 7829, 7616, 5323, 7764,
              7147, 3909, 7736, 6969, 2500, 7541, 5474, 7214, 4926, 5763, 6280, 7286, 5692, 6498, 5359, 3738, 4382,
              5491, 3935, 6095, 5405, 4823, 5012, 3557, 5343, 4997, 6438, 4638, 5404, 7908, 6958, 4689, 3468, 3050,
              8299, 5426, 3412, 5105, 6134, 4872, 5943, 6369, 5626, 3882, 2904, 3467, 3348, 4715, 5644, 6308, 4103,
              4169, 7183, 4282, 6004, 7688, 4032, 6174, 4100, 7352, 6562, 7432, 4658, 7718, 5762, 3623, 7959, 6834,
              4720, 8244, 3937, 6348, 5394, 4199, 7503, 3631, 4348, 4833, 6266, 6178, 4296, 5092, 6734, 4523, 6417,
              5654, 5170, 4300, 6248, 3221, 5246, 6913, 6155, 3529, 3136, 4497, 5091, 5846, 3020, 3057, 6181, 5273,
              4226, 3801, 7386, 5145, 5905, 6190, 6802, 6143, 7474, 8268, 7679, 8224, 7776, 7119, 6735, 4996, 3810,
              3855, 2602, 3854, 3185, 5622, 6707, 3521, 6257, 4108, 4133, 7154, 2640, 6794, 3675, 6492, 7930, 2999,
              3850, 3687, 5037, 3236, 3573, 6783, 5842, 6209, 7855, 3446, 7197, 4149, 3644, 5044, 4653, 3188, 3542,
              3160, 7879, 7048, 4622, 4010, 3100, 5691, 3410, 6286, 3847, 6785, 7187, 4142, 4505, 3435, 5710, 5269,
              5894, 5088, 4099, 7922, 6440, 4466, 8189, 6082, 6687, 5995, 6967, 4096, 4166, 6770, 6346, 4357, 6950,
              7380, 7106, 4831, 2858, 5604, 6106, 5656, 3825, 5742, 4730, 7236, 6341, 3832, 5654, 3170, 6039, 3540,
              5046, 6537, 5555, 5569, 4542, 5910, 7604, 3582, 4928, 6615, 4334, 4452, 4549, 7044, 4782, 7868, 3742,
              4042, 2563, 4039, 7052, 6481, 5414, 7341, 5676, 3806, 5366, 3698, 7260, 2871, 6692, 3556, 4636, 6319,
              5220, 6021, 8308, 5153, 8160, 6420, 3507, 3773, 5765, 4060, 2834, 5124, 5984, 5711, 3319, 6123, 7363,
              5398, 5653, 7292, 5042, 6267, 8165, 4739, 5521, 5208, 6282, 4459, 4829, 7794, 7025, 4526, 6530, 7206,
              4674, 7418, 5553, 6873, 6822, 6890, 5923, 5381, 5095, 3962, 8036, 6728, 3041, 3604, 6923, 6143, 2888,
              3254, 5022, 3029, 3395, 7674, 4021, 4260, 4487, 6503, 3636, 5039, 5977, 7326, 6589, 4913, 7009, 7717,
              5532, 7409, 3715, 4942, 7255, 7527, 5782, 8125, 7895, 7099, 4743, 6837, 2679, 5169, 6627, 3720, 4478,
              6844, 5889, 3226, 4539, 5587, 6520, 5063, 3388, 5952, 5126, 7234, 6430, 7005, 3523, 3427, 6620, 3153,
              6984, 7176, 5566, 6272, 7799, 8061, 6279, 6719, 7927, 4467, 5744, 4756, 5555, 5567, 4886, 3997, 7618,
              3753, 6420, 3259, 8108, 7492, 6977, 6811, 4051, 8347, 3476, 5767, 6119, 4190, 4883, 4938, 6999, 3945,
              3126, 5454, 4121, 6303, 3573, 5323, 3314, 4692, 2510, 5126, 5712, 5514, 5517, 5368, 6595, 8350, 5238,
              7090, 7507, 4875, 8201, 5089, 7851, 4545, 4857, 2743, 5828, 3401, 7882, 3964, 3716, 5376, 8327, 4926,
              3192, 3354, 6912, 3935, 7502, 3135, 5435, 5735, 5028, 5760, 5047, 5001, 5204, 3324, 4124, 4726, 6260,
              4333, 6999, 4396, 4570, 6313, 4300, 4837, 6011, 5235, 6958, 6359, 6379, 6757, 3155, 7359, 4740, 4868,
              7233, 7250, 6926, 6022, 5004, 4481, 5796, 4793, 3158, 2928, 4824, 5253, 5535, 2824, 7600, 6160, 6326,
              7094, 4810, 4124, 8092, 7238, 6840, 3699, 6965, 6574, 4323, 3918, 3431, 3581, 7070, 2727, 8289, 7925,
              6664, 3495, 8063, 6648, 7112, 5683, 4314, 6614, 5906, 4745, 8261, 3376, 7498, 6592, 3468, 5441, 5154,
              2542, 5708, 3931, 3625, 4979, 8239, 5575, 5561, 5253, 2641, 5506, 3163, 3655, 4207, 4455, 4604, 6749,
              4527, 4026, 3848, 5092, 3076, 6061, 6867, 5556, 5112, 3414, 2832, 7142, 6264, 6807, 7435, 6357, 3506,
              5504, 5208, 4828, 6470, 7398, 7117, 3456, 6833, 5958, 6717, 6253, 6569, 4657, 8379, 3293, 6080, 4634,
              4215, 3567, 2687, 7651, 2490, 8264, 6739, 4811, 4457, 4617, 3290, 6978, 5477, 6731, 8265, 5597, 5279,
              8209, 4314, 5038, 6419, 6512, 7626, 3398, 5716, 7116, 5347, 6790, 7528, 4784, 5428, 5248, 6755, 4870,
              4497, 6871, 4966, 4276, 4705, 2492, 8037, 6130, 3546, 4841, 6313, 4844, 5301, 8283, 5949, 6606, 4865,
              6550, 4849, 6924, 3248, 8094, 5801, 8011, 3752, 3548, 4041, 3808, 3974, 2901, 2856, 4403, 3455, 6312,
              6879, 5576, 6390, 6386, 4921, 7011, 6590, 2521, 6963, 3989, 2544, 5172, 6032, 5834, 6203, 5479, 4860,
              8358, 7473, 4368, 3013, 4023, 3888, 7028, 5858, 6416, 6675, 4218, 3666, 5793, 4480, 5260, 5657, 7226,
              2609, 3399, 7216, 5201, 4579, 4671, 5425, 3957, 3814, 5470, 8127, 4618, 5458, 6299, 5379, 7243, 7149,
              7834, 6608, 4783, 6769, 6001, 7218, 2957, 4512, 7109, 3586, 5402, 6328, 6206, 4842, 8372, 6404, 6324,
              5144, 6367, 5822, 5385, 4244, 4441, 5646, 6901, 5996, 5833, 5023, 4737, 5407, 6757, 7878, 5188, 6010,
              6631, 5468, 4085, 7424, 3719, 4242, 4919, 6132, 6062, 3881, 6246, 5795, 4245, 4580, 2896, 5098, 5746,
              6409, 7929, 5821, 3829, 5794, 5185, 6525, 5635, 4974, 2770, 5430, 7365, 4004, 2616, 3795, 5669, 5149,
              6636, 6971, 7120, 3837, 4147, 7095, 8336, 6379, 6860, 5931, 5139, 7085, 3326, 6658, 4517, 3225, 3055,
              5944, 6014, 6467, 4636, 4297, 6760, 3772, 5307, 7315, 4247, 6780, 4125, 4066, 5168, 4162, 3671, 5741,
              6120, 3525, 6333, 7983, 3678, 5525, 6727, 6841, 6255, 3399, 3146, 7353, 5119, 6693, 5810, 3943, 6929,
              4377, 7770, 5741, 6759, 8360, 2946, 6899, 5836, 4505, 7179, 4032, 6040, 7392, 6853, 4617, 3407, 6571,
              3452, 3574, 2799, 4127, 6554, 5719, 3783, 6519, 6935, 4337, 4287, 8193, 5911, 8032, 5158, 8115, 4653,
              3002, 3605, 7434, 3855, 3884, 5738, 4401, 6267, 3950, 7792, 6003, 3887, 7687, 3178, 4409, 7614, 6609,
              3007, 5679, 5806, 2746, 7898, 7412, 5401, 4230, 6096, 6339, 4169, 4897, 7005, 4628, 3871, 4517, 6607,
              5185, 3443, 4361, 2525, 2852, 3067, 7421, 5933, 7463, 5543, 4514, 4589, 2759, 7059, 5074, 4048, 4781,
              7873, 8356, 4118, 5998, 4481, 4451, 8222, 5146, 8300, 5021, 6835, 5417, 4814, 3531, 5096, 2740, 4664,
              6434, 3896, 7350, 3879, 7517, 6851, 5665, 4819, 7617, 4792, 7555, 7096, 6404, 4453, 3826, 3071, 7912,
              2772, 3923, 6685, 4747, 4981, 6907, 4637, 4404, 6702, 4795, 6661, 4717, 6213, 6205, 4460, 7006, 3560,
              3630, 7074, 4654, 4751, 5128, 8277, 6027, 4937, 4892, 5613, 7390, 6521, 6977, 5913, 7055, 7335, 5515,
              5601, 8181, 3744, 3660, 3201, 6427, 6401, 4180, 4834, 7440, 4573, 6078, 5994, 6941, 2667, 6980, 8075,
              6916, 7137, 4722, 5121, 8295, 5243, 3707, 6389, 4173, 7098, 5823, 7809, 7964, 5991, 3513, 4583, 4724,
              4651, 6300, 3794, 5559, 4942, 5111, 7062, 7272, 4451, 7585, 5192, 8215, 4059, 5531, 4385, 4663, 6426,
              3637, 7176, 3787, 7332, 6157, 4359, 5849, 4088, 2821, 3771, 8218, 6718, 5354, 5907, 5429, 4947, 4969,
              7461, 6008, 8269, 6917, 6378, 6407, 5490, 6875, 5717, 6494, 5640, 6023, 4871, 4116, 4760, 8015, 5623,
              6483, 2945, 6873, 7361, 4152, 5072, 5692, 7276, 4266, 5579, 4957, 4103, 7056, 6292, 3799, 4915, 4778,
              5675, 5935, 4226, 7063, 3058, 5513, 3287, 5035, 7612, 5255, 3011, 3379, 4863, 5670, 3826, 6727, 6098,
              3432, 4856, 6734, 3754, 5064, 4561, 2938, 4118, 4047, 3868, 2729, 6854, 4669, 7047, 5245, 6051, 5500,
              5032, 6190, 5376, 3240, 7624, 6503, 6647, 6868, 6403, 3392, 2487, 5027, 3514, 5228, 6270, 3938, 5631,
              4722, 4353, 5189, 6048, 8273, 3310, 2645, 4790, 4328, 3052, 8214, 7384, 6103, 4540, 3429, 2771, 3255,
              5843, 3420, 6679, 3411, 4174, 4363, 3872, 4884, 3298, 6304, 2944, 5436, 5029, 2599, 5672, 2987, 4762,
              6504, 6444, 4380, 4667, 6165, 6263, 4029, 7356, 4412, 3017, 4855, 8110, 5831, 3452, 8217, 6373, 6273,
              3456, 5090, 6223, 7321, 6877, 4738, 6725, 7366, 3911, 2669, 3403, 2967, 4494, 3791, 6774, 4907, 4330,
              4462, 6471, 4102, 6458, 6534, 6732, 8147, 7024, 6387, 6400, 4630, 5494, 4037, 4465, 7800, 6188, 3598,
              4229, 3759, 6395, 5832, 5461, 6933, 7524, 4977, 5704, 2796, 4848, 6294, 4202, 7027, 7769, 6703, 2545,
              5054, 4759, 3413, 7103, 6165, 2782, 4503, 6707, 7374, 6925, 5366, 6669, 2784, 6770, 7207, 5908, 6755,
              3864, 5994, 5011, 4778, 6198, 7453, 5621, 5237, 3568, 6586, 2738, 5217, 6834, 4974, 4184, 3603, 5173,
              7092, 6722, 6554, 5178, 6476, 5588, 6817, 3907, 6374, 4595, 4658, 4494, 5702, 4788, 5297, 5455, 8023,
              7491, 3767, 7049, 3522, 8136, 3892, 6778, 5228, 6652, 4806, 7810, 8197, 6055, 4195, 5983, 6125, 3794,
              3123, 5784, 3863, 4536, 6524, 5917, 4521, 4878, 4113, 3715, 5952, 4788, 4181, 6709, 6831, 7064, 5198,
              3545, 5791, 3129, 4072, 4676, 6597, 2659, 7319, 3181, 6397, 3045, 3898, 7500, 5584, 5084, 6932, 6410,
              6206, 6361, 4443, 5556, 7373, 5904, 6717, 7198, 4686, 4587, 7205, 6392, 6247, 5388, 4304, 5353, 7217,
              7277, 6053, 7944, 4214, 5174, 6639, 6025, 5780, 4566, 5110, 3059, 6214, 4725, 7573, 2704, 2570, 5748,
              4990, 8171, 6037, 5140, 8369, 5084, 4388, 5203, 6145, 4252, 5793, 5788, 5391, 2733, 5189, 4120, 8242,
              5950, 2800, 8077, 6726, 5017, 7847, 4030, 7019, 4950, 6127, 4354, 6018, 3820, 3682, 5831, 6151, 5053,
              5553, 5060, 4468, 6602, 5611, 6604, 8252, 7125, 4623, 3780, 4349, 4375, 5747, 4009, 8326, 3454, 5596,
              6329, 5591, 7784, 4394, 6728, 4916, 4915, 3393, 5316, 4817, 8113, 3335, 5723, 4825, 6530, 5652, 5025,
              3228, 2812, 6070, 5869, 6800, 6493, 3928, 6071, 5263, 3104, 2515, 5835, 5872, 5755, 4985, 6214, 5089,
              3099, 3777, 7843, 4149, 2765, 6702, 6244, 2889, 3572, 4346, 7093, 3213, 4908, 4289, 2934, 8234, 6743,
              7551, 7713, 7410, 7053, 4439, 6947, 7322, 6516, 3532, 5182, 5857, 4157, 7435, 4599, 6642, 5175, 2590,
              7313, 6864, 6162, 2642, 3241, 4303, 6830, 6127, 6800, 6469, 4492, 7149, 6331, 7224, 5472, 5933, 2919,
              4531, 4870, 3246, 5278, 2530, 6108, 3250, 5744, 5271, 5560, 6593, 7714, 7850, 6487, 4077, 4853, 6866,
              5462, 3249, 5713, 3567, 3214, 4838, 3433, 4585, 2652, 4726, 4335, 5138, 4225, 7256, 3470, 5874, 3009,
              6772, 4199, 4049, 3927, 3449, 5474, 3191, 6208, 5094, 6603, 6992, 7298, 4330, 3077, 6935, 4201, 5923,
              6082, 4691, 5402, 2787, 7290, 3366, 5462, 3788, 8026, 4323, 6063, 6070, 3272, 5557, 6549, 7874, 6290,
              4932, 7000, 6410, 7348, 5027, 3014, 3451, 6740, 8231, 3513, 5573, 4164, 7011, 6540, 4044, 3169, 5606,
              7131, 5532, 8096, 6481, 3048, 3460, 6506, 3134, 5852, 7404, 4354, 7841, 4496, 6863, 5139, 3070, 4529,
              5213, 2638, 5440, 5167, 6824, 3901, 6411, 2794, 5975, 3751, 8166, 3596, 4703, 4519, 4887, 5955, 4364,
              7613, 4585, 5795, 4659, 6075, 5521, 7151, 5397, 2495, 7299, 5630, 2615, 4105, 5488, 2953, 6776, 5538,
              3758, 4876, 3421, 3764, 6505, 3888, 5613, 2701, 7313, 4491, 2685, 4979, 3536, 6077, 5130, 3179, 6397,
              6415, 6815, 7653, 8148, 4628, 8126, 3271, 7132, 7377, 6945, 4781, 6849, 3493, 2970, 6089, 3613, 3725,
              6114, 5251, 7442, 3987, 5986, 6136, 4716, 2869, 3400, 7302, 3210, 5509, 5512, 7257, 4805, 5743, 6708,
              6560, 3103, 7791, 4769, 8156, 6013, 6947, 5276, 5900, 7755, 6012, 3509, 5003, 3464, 6156, 3817, 6372,
              3628, 3805, 3626, 4709, 7823, 4755, 8352, 2766, 6344, 6860, 5372, 6281, 7346, 3128, 6829, 7016, 3176,
              3768, 3669, 4978, 3853, 2811, 7332, 8314, 5820, 3601, 3663, 7978, 4568, 4756, 4308, 5488, 5530, 6902,
              4698, 4952, 7196, 2726, 3494, 6164, 5181, 6094, 4841, 7955, 3572, 3889, 3551, 7952, 6895, 2850, 5827,
              3543, 4862, 5326, 4989, 7924, 2793, 5749, 6832, 5826, 6914, 3418, 5574, 4725, 4344, 3867, 4892, 2962,
              6864, 7512, 6064, 5194, 7091, 4027, 2572, 3890, 5501, 4820, 6083, 2788, 5364, 8054, 3518, 6202, 6653,
              4302, 7439, 4385, 7119, 7523, 3208, 3972, 4165, 3401, 3642, 2508, 5257, 5612, 5946, 3510, 6100, 6063,
              5618, 3501, 6753, 6887, 3943, 7159, 5021, 8228, 7676, 4731, 6956, 4960, 7168, 5838, 5775, 4108, 6166,
              5120, 4900, 8086, 8180, 3844, 4678, 3822, 3365, 7169, 4866, 3765, 6237, 4802, 5238, 7185, 3739, 6395,
              4665, 2819, 5999, 3859, 7436, 6128, 5545, 3027, 5219, 4902, 4643, 7440, 8291, 4975, 6322, 6634, 4390,
              7361, 6179, 7214, 6462, 7130, 3458, 4146, 6362, 4015, 4203, 4341, 3937, 4014, 6923, 3492, 7781, 7594,
              5811, 3721, 5390, 6468, 3981, 5601, 5725, 6632, 6579, 5066, 4253, 7376, 7733, 7457, 6964, 4224, 6391,
              4256, 5607, 4070, 3721, 8274, 5918, 8322, 2855, 6210, 4111, 5083, 2899, 4406, 4953, 4977, 7090, 6752,
              6998, 5447, 3097, 4522, 5430, 6617, 3425, 3484, 3651, 6833, 2566, 7364, 6212, 5016, 4398, 7442, 6649,
              6256, 2815, 5756, 2996, 2499, 8031, 5236, 5204, 2584, 6662, 6310, 3661, 6801, 5291, 4723, 5941, 5310,
              4264, 7722, 6567, 5018, 4513, 3333, 5397, 4618, 3132, 3360, 5550, 4475, 8332, 7973, 3841, 5920, 7596,
              6665, 7798, 4552, 6207, 5019, 6979, 3408, 6092, 4148, 5783, 4871, 7288, 7574, 6911, 4347, 7069, 3740,
              6094, 4116, 6656, 3023, 5785, 6961, 7391, 7349, 6704, 4953, 6017, 5138, 4434, 3497, 6030, 5802, 6453,
              5936, 4242, 4429, 5034, 6493, 6360, 6383, 6634, 5274, 7505, 5166, 5048, 4050, 4150, 6195, 6868, 8170,
              7824, 3091, 7007, 3611, 5932, 3554, 7609, 4482, 2836, 4277, 7742, 8045, 5917, 5002, 5377, 7564, 4742,
              7036, 3629, 4209, 5628, 3516, 6270, 6194, 4668, 7415, 6468, 6232, 4090, 5959, 3212, 2974, 6729, 5007,
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              5762, 5373, 4157, 6910, 2831, 4846, 6709, 4661, 3531, 4737, 5266, 7968, 3994, 3395, 6148, 5840, 6294,
              6953, 3407, 7455, 3828, 8188, 7097, 4754, 7108, 5128, 6388, 4416, 7891, 2818, 3453, 5295, 4861, 5623,
              7743, 3614, 6430, 3712, 6560, 6761, 6866, 4252, 4469, 3749, 5926, 7408, 4745, 7686, 7875, 3726, 4246,
              6887, 4404, 5534, 5924, 4746, 3845, 2681, 4248, 5326, 4234, 7239, 6184, 5357, 5698, 7543, 5234, 2905,
              7046, 3735, 6250, 3849, 5341, 6325, 6402, 5869, 5499, 4858, 7308, 6495, 4843, 7206, 3497, 6465, 5727,
              4035, 7114, 5360, 5293, 5648, 5141, 5610, 3183, 3105, 3831, 3156, 4768, 3491, 8211, 5993, 6592, 5774,
              3740, 3593, 3956, 5164, 7232, 6225, 2847, 6768, 4180, 5188, 7293, 8017, 3096, 7486, 4947, 3705, 8116,
              3592, 7221, 4065, 3654, 6627, 4046, 5898, 6154, 3734, 2497, 2549, 4970, 4741, 3281, 5335, 7465, 6431,
              3737, 4057, 5061, 6744, 5410, 4989, 7165, 8159, 4773, 6824, 6886, 4011, 6750, 3961, 2476, 6777, 4192,
              4012, 4720, 4030, 3754, 5290, 2978, 7101, 4143, 7317, 3959, 3457, 2914, 4106, 6076, 3982, 7452, 3668,
              4417, 5320, 7579, 2716, 4381, 4472, 3074, 7021, 7151, 5058, 3391, 3519, 5361, 4425, 6308, 5774, 6946,
              7347, 8202, 3267, 2745, 6437, 6872, 4022, 3961, 4889, 7870, 7102, 5583, 5375, 7154, 4593, 2961, 5905,
              5699, 2689, 4856, 5837, 7282, 6183, 3527, 6683, 6586, 4559, 7323, 6170, 8184, 3687, 2893, 3189, 5094,
              4627, 5849, 5727, 3008, 6637, 7763, 5015, 4700, 2622, 3806, 3448, 2644, 4228, 3503, 5157, 5476, 6983,
              5290, 6919, 7014, 5967, 5526, 4126, 5647, 4455, 6623, 7265, 6309, 3634, 3953, 4083, 6073, 3252, 4924,
              5543, 3352, 3778, 5484, 4674, 6158, 6329, 7712, 2918, 7140, 7195, 8304, 6529, 2779, 5270, 4059, 7905,
              5258, 4772, 5928, 7156, 3969, 2993, 7088, 4685, 7375, 3368, 7953, 7790, 3857, 4119, 7977, 5569, 7707,
              2608, 5425, 3985, 4161, 3906, 6515, 7422, 8290, 5904, 4697, 6454, 5344, 5758, 5767, 5988, 4572, 4094,
              4514, 6325, 3629, 6597, 6077, 7330, 6713, 7699, 5746, 7782, 6673, 7366, 6245, 7987, 4196, 7740, 8140,
              3779, 3012, 4826, 5029, 4028, 6315, 2931, 5558, 7592, 7032, 4160, 2923, 5346, 7284, 7029, 4057, 4721,
              6005, 7329, 6285, 5564, 3827, 7382, 7368, 7487, 5380, 5062, 4804, 3677, 4917, 6552, 4803, 3588, 3544,
              3849, 5863, 6439, 4349, 4263, 5360, 7016, 6543, 4713, 7932, 6892, 3634, 6268, 2516, 4270, 3562, 5571,
              6186, 4577, 3562, 5754, 7031, 4912, 5596, 3479, 4078, 4646, 5239, 4882, 7045, 5570, 7291, 6152, 2939,
              2924, 4375, 3483, 7270, 5196, 6117, 4326, 5206, 5942, 4994, 6661, 5392, 6035, 6184, 5205, 7146, 5844,
              6091, 4132, 4198, 3474, 7248, 8226, 5170, 4614, 3775, 7677, 3592, 7534, 5009, 4046, 3101, 5557, 7318,
              7297, 4984, 5162, 4172, 4506, 5988, 3385, 3723, 4326, 4151, 4661, 4640, 3621, 3972, 3042, 5285, 7272,
              7518, 5330, 6115, 4080, 6199, 8039, 6532, 7294, 8131, 2484, 6347, 2702, 6678, 4534, 2719, 7408, 4898,
              6685, 4508, 5637, 2736, 6032, 3919, 3677, 4809, 7035, 5829, 5918, 6274, 3329, 8111, 4364, 6973, 4597,
              4038, 5286, 4736, 4866, 7817, 3114, 2883, 3653, 6326, 3822, 4801, 2983, 3350, 7277, 6712, 3807, 5697,
              6995, 3912, 4601, 2806, 3881, 5722, 3770, 7615, 7576, 5681, 6474, 3496, 5926, 7105, 3079, 4115, 3958,
              4839, 6228, 4245, 6478, 3764, 4776, 3920, 4965, 5781, 6183, 4438, 5701, 7450, 5689, 4461, 7537, 6051,
              8240, 7825, 3282, 6306, 4783, 3485, 3787, 8191, 4420, 4439, 5729, 7387, 4656, 4824, 6799, 3833, 5059,
              7279, 6233, 7449, 6337, 6425, 5909, 4957, 5549, 7224, 7975, 4564, 4854, 6736, 4767, 7644, 5508, 5832,
              5731, 4190, 6362, 4930, 3475, 6940, 5236, 5505, 5433, 6522, 5142, 5081, 5578, 3330, 7331, 5041, 7371,
              5364, 6643, 4662, 3803, 6455, 3802, 6378, 3695, 3796, 3046, 3563, 4581, 5489, 5049, 5297, 3499, 5659,
              5192, 4013, 7910, 5772, 6371, 4109, 3610, 7244, 5457, 4621, 5702, 3450, 5968, 5066, 6700, 5818, 5713,
              7188, 5922, 6155, 4246, 3960, 6116, 4168, 6204, 3040, 5945, 4320, 7419, 7343, 4712, 7304, 5318, 3798,
              5830, 5466, 4143, 7278, 3675, 6822, 4851, 6408, 7803, 7367, 4035, 6471, 5528, 6989, 7661, 2862, 5104,
              5600, 5700, 4402, 6523, 6019, 5887, 7788, 3680, 5737, 6522, 4318, 7445, 3946, 4693, 6938, 7170, 2913,
              7189, 5090, 6201, 7907, 3647, 3758, 8272, 7104, 5197, 3798, 3514, 5808, 7900, 3956, 7035, 4273, 5887,
              3454, 7182, 7970, 4500, 4037, 5580, 5805, 3597, 7954, 4531, 5086, 2758, 6332, 3992, 4704, 5502, 6582,
              6380, 5646, 7328, 7685, 6645, 5529, 3839, 5413, 3576, 3561, 4394, 3394, 6102, 6566, 6812, 6293, 6050,
              6090, 3926, 5853, 6088, 3168, 6967, 5289, 6937, 7716, 5201, 2995, 7656, 6986, 5903, 7506, 7865, 3444,
              6801, 5354, 6730, 3302, 5951, 6472, 3343, 3207, 3979, 7089, 7641, 4724, 4370, 5541, 6501, 4099, 5276,
              6984, 4187, 4362, 5383, 6578, 3856, 6409, 4525, 4931, 2569, 3971, 3672, 3944, 5527, 4156, 5630, 4944,
              5529, 6391, 3390, 7866, 6965, 7134, 7067, 6110, 6405, 4794, 6204, 2603, 6839, 6224, 4389, 6827, 5888,
              2698, 8256, 6150, 4128], W=5000))


if __name__ == '__main__':
    main()
